{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T22:33:34Z","timestamp":1757543614531,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["Grant No. F2019203157"],"award-info":[{"award-number":["Grant No. F2019203157"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Research Project of Hebei Higher Education Institutions","award":["Grant No. ZD2019004","No. QN2018074"],"award-info":[{"award-number":["Grant No. ZD2019004","No. QN2018074"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant No. 61871465","No. 61602401"],"award-info":[{"award-number":["Grant No. 61871465","No. 61602401"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cluster Comput"],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The application of evolutionary game method to study user behavior in social networks is a current hot issue. Most of the current evolutionary game models are proposed based on the game between nodes, which cannot accurately describe the diverse behaviors of users, and ignores the influence of network dynamics on evolutionary game. In order to solve the above problems, an edge evolution game (EEG) model is proposed in this paper. Firstly, the edge game model combines the pairwise interaction mode with the prisoner\u2019s dilemma payoff matrix to calculate the user income. Secondly, on the basis of strategy update, the disconnect\u2013reconnect mechanism is proposed to promote the updating of user relationship. In this mechanism, nodes perform the disconnect\u2013reconnect based on the incomes: the betrayal neighbor with the lowest incomes is disconnected, and the neighbor of the disconnected neighbor with the highest incomes is reconnected. Finally, three kinds of networks are selected for experimental verification. The experimental results show that the cooperation clusters are formed in all three kinds of networks, which greatly promote the cooperation evolution among users.<\/jats:p>","DOI":"10.1007\/s10586-022-03612-4","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T20:02:38Z","timestamp":1658520158000},"page":"4397-4412","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["User behavior analysis based on edge evolutionary game model in social network"],"prefix":"10.1007","volume":"25","author":[{"given":"Jing","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3411-7181","authenticated-orcid":false,"given":"Hongbo","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nana","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingxin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"issue":"7","key":"3612_CR1","first-page":"1369","volume":"57","author":"YX Yu","year":"2020","unstructured":"Yu, Y.X., Liu, M., Zhang, H.Y.: Research on user behavior understanding and personalized service recommendation algorithm in Twitter social networks. J. Comput. Res. Dev. 57(7), 1369\u20131380 (2020)","journal-title":"J. Comput. Res. Dev."},{"issue":"5","key":"3612_CR2","first-page":"96","volume":"35","author":"JD Liu","year":"2013","unstructured":"Liu, J.D., Liu, Y.M.: Herding behavior of network public opinion communication based on incomplete information evolutionary game model. J. Natl Univ. Def. Technol. 35(5), 96\u2013101 (2013)","journal-title":"J. Natl Univ. Def. Technol."},{"key":"3612_CR3","first-page":"28","volume":"1","author":"XC Wei","year":"2020","unstructured":"Wei, X.C., Zhu, T.: Coordinated mechanism of E-commerce ecosystem based on evolutionary game. J. Beijing Univ. Posts Telecommun. 1, 28\u201340 (2020)","journal-title":"J. Beijing Univ. Posts Telecommun."},{"key":"3612_CR4","doi-asserted-by":"crossref","unstructured":"Liu, F., Pan, L., Yao, L.: Evolutionary game based analysis for user privacy protection behaviors in social networks. In: 2018 IEEE Third International Conference on Data Science in Cyberspace (DSC), pp. 274\u2013279. IEEE (2018)","DOI":"10.1109\/DSC.2018.00046"},{"issue":"7649","key":"3612_CR5","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1038\/nature21723","volume":"544","author":"B Allen","year":"2017","unstructured":"Allen, B., Lippner, G., Chen, Y.T., Fotouhi, B., Momeniet, N.: Evolutionary dynamics on any population structure. Nature 544(7649), 227\u2013230 (2017)","journal-title":"Nature"},{"issue":"4","key":"3612_CR6","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1007\/s00285-018-1305-z","volume":"78","author":"B Allen","year":"2019","unstructured":"Allen, B., McAvoy, A.: A mathematical formalism for natural selection with arbitrary spatial and genetic structure. J. Math. Biol. 78(4), 1147\u20131210 (2019)","journal-title":"J. Math. Biol."},{"issue":"7713","key":"3612_CR7","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1038\/s41586-018-0277-x","volume":"559","author":"C Hilbe","year":"2018","unstructured":"Hilbe, C., \u0160imsa, \u0160, Chatterjee, K., Nowak, M.A.: Evolution of cooperation in stochastic games. Nature 559(7713), 246\u2013249 (2018)","journal-title":"Nature"},{"key":"3612_CR8","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1016\/j.physa.2018.06.053","volume":"509","author":"DY Jia","year":"2018","unstructured":"Jia, D.Y., Jin, J.H., Du, C.P., Shi, L.: Effects of inertia on the evolution of cooperation in the voluntary prisoner\u2019s dilemma game. Physica A 509, 817\u2013826 (2018)","journal-title":"Physica A"},{"key":"3612_CR9","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.chaos.2018.02.035","volume":"109","author":"H Guo","year":"2018","unstructured":"Guo, H., Chu, C., Shen, C., Lei, S.: Reputation-based coevolution of link weights promotes cooperation in spatial prisoner\u2019s dilemma game. Chaos Solitons Fractals 109, 265\u2013268 (2018)","journal-title":"Chaos Solitons Fractals"},{"key":"3612_CR10","doi-asserted-by":"crossref","unstructured":"Xu, X., Rong, Z., Tse, C.K.: Bounded rationality optimizes the performance of networked systems in prisoner\u2019s dilemma game. In: IEEE International Symposium on Circuits and Systems (ISCAS), 2018, pp. 1\u20135. IEEE (2018)","DOI":"10.1109\/ISCAS.2018.8351860"},{"key":"3612_CR11","first-page":"437","volume":"320","author":"Y Li","year":"2018","unstructured":"Li, Y., Zhang, J., Perc, M.: Effects of compassion on the evolution of cooperation in spatial social dilemmas. Appl. Math. Comput. 320, 437\u2013443 (2018)","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"3612_CR12","doi-asserted-by":"publisher","first-page":"1006947","DOI":"10.1371\/journal.pcbi.1006947","volume":"15","author":"Q Su","year":"2019","unstructured":"Su, Q., Zhou, L., Wang, L.: Evolutionary multiplayer games on graphs with edge diversity. PLoS Comput. Biol. 15(4), 1006947 (2019)","journal-title":"PLoS Comput. Biol."},{"issue":"2","key":"3612_CR13","doi-asserted-by":"publisher","first-page":"020203","DOI":"10.1088\/1674-1056\/28\/2\/020203","volume":"28","author":"XJ Wang","year":"2019","unstructured":"Wang, X.J., Gu, C.L., Lv, S.J., Quan, J.: Evolutionary game dynamics of combining the Moran and imitation processes. Chin. Phys. B 28(2), 020203 (2019)","journal-title":"Chin. Phys. B"},{"issue":"2","key":"3612_CR14","doi-asserted-by":"publisher","first-page":"e0193151","DOI":"10.1371\/journal.pone.0193151","volume":"13","author":"C Shen","year":"2018","unstructured":"Shen, C., Chu, C., Geng, Y., Jin, J., Chen, F., Shi, L.: Cooperation enhanced by the coevolution of teaching activity in evolutionary prisoner\u2019s dilemma games with voluntary participation. PLoS ONE 13(2), e0193151 (2018)","journal-title":"PLoS ONE"},{"key":"3612_CR15","doi-asserted-by":"crossref","unstructured":"Yu, J., Wang, Y., Li, J., Shen, H., Cheng, X.: Analysis of competitive information dissemination in social network based on evolutionary game model. In: Cloud and Green Computing (CGC), pp. 748\u2013753. IEEE (2012)","DOI":"10.1109\/CGC.2012.126"},{"key":"3612_CR16","doi-asserted-by":"publisher","first-page":"679726.1","DOI":"10.1155\/2015\/679726","volume":"2015","author":"Q Sun","year":"2015","unstructured":"Sun, Q., Yao, Z.: Evolutionary game analysis of competitive information dissemination on social networks: an agent-based computational approach. Math. Probl. Eng. 2015, 679726.1-679726.12 (2015)","journal-title":"Math. Probl. Eng."},{"issue":"1","key":"3612_CR17","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1002\/sec.535","volume":"6","author":"YZ Wang","year":"2013","unstructured":"Wang, Y.Z., Li, J.Y., Meng, K., Lin, C., Cheng, X.Q.: Modeling and security analysis of enterprise network using attack\u2013defense stochastic game Petri nets. Secur. Commun. Netw. 6(1), 89\u201399 (2013)","journal-title":"Secur. Commun. Netw."},{"key":"3612_CR18","doi-asserted-by":"crossref","unstructured":"Su, J.H., Fang, M., Jiang, J., Chen, Y.W.: An evolutionary game model of multi-topics diffusion in social network. In: The 4th Annual International Conference on Information Technology and Applications (ITA 2017), vol. 12, p. 03045 (2017)","DOI":"10.1051\/itmconf\/20171203045"},{"key":"3612_CR19","doi-asserted-by":"publisher","first-page":"18001","DOI":"10.1209\/0295-5075\/126\/18001","volume":"126","author":"LM Zhang","year":"2019","unstructured":"Zhang, L.M., Huang, C.W., Li, H.H., Dai, Q.L.: Aspiration-dependent strategy persistence promotes cooperation in spatial prisoner\u2019s dilemma game. Europhys. Lett. 126, 18001 (2019)","journal-title":"Europhys. Lett."},{"issue":"1","key":"3612_CR20","doi-asserted-by":"publisher","first-page":"012301","DOI":"10.1103\/PhysRevE.95.012301","volume":"95","author":"H Wu","year":"2017","unstructured":"Wu, H., Arenas, A., G\u00f3mez, S.: Influence of trust in the spreading of information. Phys. Rev. E 95(1), 012301 (2017)","journal-title":"Phys. Rev. E"},{"issue":"001","key":"3612_CR21","first-page":"223","volume":"46","author":"JY Yu","year":"2018","unstructured":"Yu, J.Y., Wang, Y.Z., Jin, X.L.: Evolutionary analysis on information sharing behavior in social networks based on social evolutionary game. Acta Electron. Sin. 46(001), 223\u2013229 (2018)","journal-title":"Acta Electron. Sin."},{"key":"3612_CR22","doi-asserted-by":"publisher","first-page":"108703","DOI":"10.1088\/1674-1056\/ab3f1e","volume":"28","author":"JW Wang","year":"2019","unstructured":"Wang, J.W., He, J.L., Yu, F.Y., Chen, W., Wang, R., Yu, K.: Benefit community promotes evolution of cooperation in prisoners\u2019 dilemma game. Chin. Phys. B 28, 108703 (2019)","journal-title":"Chin. Phys. B"},{"key":"3612_CR23","doi-asserted-by":"publisher","first-page":"065102","DOI":"10.1103\/PhysRevE.69.065102","volume":"69","author":"MG Zimmermann","year":"2004","unstructured":"Zimmermann, M.G., Eguluz, V.M., Miguel, M.S.: Coevolution of dynamical states and interactions in dynamic networks. Phys. Rev. E 69, 065102 (2004)","journal-title":"Phys. Rev. E"},{"key":"3612_CR24","doi-asserted-by":"publisher","first-page":"056118","DOI":"10.1103\/PhysRevE.72.056118","volume":"69","author":"MG Zimmermann","year":"2005","unstructured":"Zimmermann, M.G., Eguluz, V.M.: Cooperation, social networks, and the emergence of leadership in a prisoner\u2019s dilemma with adaptive local interactions. Phys. Rev. E 69, 056118 (2005)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"3612_CR25","doi-asserted-by":"publisher","first-page":"e11187","DOI":"10.1371\/journal.pone.0011187","volume":"5","author":"B Wu","year":"2010","unstructured":"Wu, B., Zhou, D., Fu, F., Luo, Q.J., Wang, L., Traulsen, A.: Evolution of cooperation on stochastic dynamical networks. PLoS ONE 5(6), e11187 (2010)","journal-title":"PLoS ONE"},{"key":"3612_CR26","doi-asserted-by":"publisher","first-page":"098901","DOI":"10.1088\/0256-307X\/35\/9\/098901","volume":"35","author":"AZ Liu","year":"2018","unstructured":"Liu, A.Z., Zhang, Y.L., Sun, C.Y., Wang, L., Traulsen, A.: Way of breaking links in the evolution of cooperation. Chin. Phys. Lett. 35, 098901 (2018)","journal-title":"Chin. Phys. Lett."},{"issue":"5","key":"3612_CR27","first-page":"58002","volume":"113","author":"JQ Li","year":"2016","unstructured":"Li, J.Q., Zhang, C.Y., Sun, Q.L., Chen, Z.Q., Zhang, J.L.: Changing intensity of interaction can resolve prisoner\u2019s dilemmas. PLoS ONE 113(5), 58002 (2016)","journal-title":"PLoS ONE"},{"key":"3612_CR28","doi-asserted-by":"publisher","first-page":"028901","DOI":"10.1088\/0256-307X\/34\/2\/028901","volume":"34","author":"CQ Chen","year":"2017","unstructured":"Chen, C.Q., Dai, Q.L., Han, C.W., Yang, J.Z., Wang, L., Traulsen, A.: Evolutionary games in two-layer networks with the introduction of dominant strategy. Chin. Phys. Lett. 34, 028901 (2017)","journal-title":"Chin. Phys. Lett."},{"key":"3612_CR29","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1038\/nphys2327","volume":"8","author":"T Nepusz","year":"2012","unstructured":"Nepusz, T., Vicsek, T.: Controlling edge dynamics in complex networks. Nat. Phys. 8, 568\u2013573 (2012)","journal-title":"Nat. Phys."},{"key":"3612_CR30","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.jtbi.2018.01.021","volume":"442","author":"Q Su","year":"2018","unstructured":"Su, Q., Li, A., Wang, L.: Evolution of cooperation with interactive identity and diversity. J. Theor. Biol. 442, 149\u2013157 (2018)","journal-title":"J. Theor. Biol."},{"issue":"4","key":"3612_CR31","doi-asserted-by":"publisher","first-page":"e1006947","DOI":"10.1371\/journal.pcbi.1006947","volume":"15","author":"Q Su","year":"2019","unstructured":"Su, Q., Zhou, L., Wang, L.: Evolutionary multiplayer games on graphs with edge diversity. PLoS Comput. Biol. 15(4), e1006947 (2019)","journal-title":"PLoS Comput. Biol."},{"issue":"6","key":"3612_CR32","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1140\/epjb\/s10051-021-00136-5","volume":"94","author":"X Li","year":"2021","unstructured":"Li, X., Cheng, L., Niu, X., Li, S., Zhu, P.: Highly cooperative individuals\u2019 clustering property in myopic strategy groups. Eur. Phys. J. B 94(6), 126 (2021)","journal-title":"Eur. Phys. J. B"},{"key":"3612_CR33","doi-asserted-by":"publisher","first-page":"052825","DOI":"10.1103\/PhysRevE.90.052825","volume":"90","author":"A CaRdillo","year":"2014","unstructured":"CaRdillo, A., Petri, G., Nicosia, V., Sinatra, R.: Evolutionary dynamics of time-resolved social interactions. Phys. Rev. E 90, 052825 (2014)","journal-title":"Phys. Rev. E"}],"container-title":["Cluster Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-022-03612-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10586-022-03612-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10586-022-03612-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T14:36:00Z","timestamp":1666881360000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10586-022-03612-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,22]]},"references-count":33,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["3612"],"URL":"https:\/\/doi.org\/10.1007\/s10586-022-03612-4","relation":{},"ISSN":["1386-7857","1573-7543"],"issn-type":[{"type":"print","value":"1386-7857"},{"type":"electronic","value":"1573-7543"}],"subject":[],"published":{"date-parts":[[2022,7,22]]},"assertion":[{"value":"24 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}